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Question About Direct Sums and Dimension

score 30 · Answer 1 · 2018-10-23 19:44:04

30

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Question About Direct Sums and Dimension

Published on 23 Oct 2018 - 19:44

score 988 · Answer 2 · 2026-03-25 03:23:00

988

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Associativity of direct sums

Published on 25 Mar 2026 - 3:23

score 197 · Answer 3 · 2018-10-30 23:31:22

Let $R$ be a ring, $M$ an $R$-module, and $A, B ≤ M$ two submodules of $M$ such that $M = A ⊕ B$. Prove that $M/A \cong B$.

score 317 · Answer 4 · 2026-03-26 06:19:39

317

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Direct Sum and Diagonalization with a Linear Map

Published on 26 Mar 2026 - 6:19

score 61 · Answer 5 · 2018-11-02 17:12:29

61

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If $S_1,S_2,S_3$ have direct sum, then, $S_1 = (S_1+S_2) \cap (S_1+S_3)$?

Published on 02 Nov 2018 - 17:12

score 990 · Answer 6 · 2018-11-06 01:23:31

990

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Let $T: V \to V$ be a linear map such that $T^2-3T+2I=0$.

Published on 06 Nov 2018 - 1:23

score 75 · Answer 7 · 2018-11-08 15:30:47

75

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A different definition of coproduct in a category

Published on 08 Nov 2018 - 15:30

score 43 · Answer 8 · 2018-11-10 03:05:01

43

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Clarifying $\oplus$ notation for modules and vector spaces?

Published on 10 Nov 2018 - 3:05

score 358 · Answer 9 · 2018-11-12 03:46:50

358

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Direct sum of Banach Spaces

Published on 12 Nov 2018 - 3:46

score 69 · Answer 10 · 2018-11-13 08:08:42

69

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If $M$ has a largest proper submodule, then $ M$ is directly indecomposable

Published on 13 Nov 2018 - 8:08

score 812 · Answer 11 · 2018-11-13 22:04:55

812

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Does a direct subtraction of vector subspaces make sense?

Published on 13 Nov 2018 - 22:04

score 82 · Answer 12 · 2018-11-16 01:11:54

$M_1$, $M_2$ are submodules of a module $M$, then $M = M_1 + M_2$ and $M_1 \cap M_2 = 0$ implies M is isomorphic to $M_1 \oplus M_2$?

score 124 · Answer 13 · 2018-11-19 20:21:33

124

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Finite Length Modules

Published on 19 Nov 2018 - 20:21

score 53 · Answer 14 · 2018-11-25 19:58:27

53

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How to show that if $X=M \oplus N$ is a Banach space then $\exists c > 0$ $\forall m\in M \, \forall n\in N: ||m||+||n|| \leq c ||m+n||$?

Published on 25 Nov 2018 - 19:58

score 362 · Answer 15 · 2018-11-26 21:07:34

362

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If $AB=0$ for two commuting linear operators and their kernels intersect trivially, do they span the whole vector space?

Published on 26 Nov 2018 - 21:07

List Question

Question About Direct Sums and Dimension

Associativity of direct sums

Let $R$ be a ring, $M$ an $R$-module, and $A, B ≤ M$ two submodules of $M$ such that $M = A ⊕ B$. Prove that $M/A \cong B$.

Direct Sum and Diagonalization with a Linear Map

If $S_1,S_2,S_3$ have direct sum, then, $S_1 = (S_1+S_2) \cap (S_1+S_3)$?

Let $T: V \to V$ be a linear map such that $T^2-3T+2I=0$.

A different definition of coproduct in a category

Clarifying $\oplus$ notation for modules and vector spaces?

Direct sum of Banach Spaces

If $M$ has a largest proper submodule, then $ M$ is directly indecomposable

Does a direct subtraction of vector subspaces make sense?

$M_1$, $M_2$ are submodules of a module $M$, then $M = M_1 + M_2$ and $M_1 \cap M_2 = 0$ implies M is isomorphic to $M_1 \oplus M_2$?

Finite Length Modules

How to show that if $X=M \oplus N$ is a Banach space then $\exists c > 0$ $\forall m\in M \, \forall n\in N: ||m||+||n|| \leq c ||m+n||$?

If $AB=0$ for two commuting linear operators and their kernels intersect trivially, do they span the whole vector space?

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